A cartoon illustrating how repeats of action potential sequences in a cortical network can be recorded in a single neuron.

The picture depicts a pyramidal neuron being recorded with an intracellular electrode that measures postsynaptic currents (PSCs) during voltage clamp recordings. A series of action potentials in three neurons forming synapses with the neuron can be recorded. The blue trace represents such a sequence that was recorded, and the red trace shows the same sequence repeating at some later time in the recording.

This briefly describes the method for repeat detection used in both Ikegaya et al. (2004) and Mokeichev et al. (2007). (A) LRI search. The entire recording is searched with a nested loop template matching algorithm where each one second interval is compared with nearly every other one second interval using cross-covariance. If the cross-covariance measured between two 1 second segments is beyond a set threshold, then the respective intervals are saved for a subsequent analysis. In this figure, two such segments are highlighted, indicating the motif (blue) and subsequent putative repeat (red). (B) The captured segments from the LRI search above are aligned, superimposed and analyzed with an HRI scan. A 100 msec window, the estimated length of an average PSP, is used to compare all 100 msec intervals between this motif-repeat pair, again using cross-covariance (h function), normalized by the respective amplitudes of the intervals (eq. 2). The final HRI is then computed (eq. 3).

We then analyzed the traces used in Ikegaya et al. (2004), using the same methods, and reportnearlyopposite results with regards to phase randomization surrogate trace generation and Poisson PSC surrogates. These recordings consistedmainly of intracellular voltage-clamp recordings from layer 5 pyramidal cells of mouse primary visual cortex slices, in vitro. The repeats found in the original recording showedhigher HRI values than any of the 50 surrogates created via phase randomization (Fig. 3A). We next re-tested the same in vivocurrent-clamp recording from a neuron in primary visual cortex of anesthetized cats, the same data used in Ikegaya et al. (2004). Using phase randomization surrogates, there were clearly more motifs found in the original trace, rejecting the null hypothesis for stochasticity (Fig. 3B). This does not conflict with findings from Mokeichev et al. (2007) as this test on cat in vivo data was not reported in that study.

Figure 3

Phase randomized surrogates display many fewer repeats than original traces.

(A) An 8-min voltage-clamp trace recorded from a layer 5 pyramidal cell in a mouse visual cortex slice (red) was compared to fifty surrogates generated by phase randomization (blue). Trace segments that gave the highest HRI values are shown in the top panels, and the HRI sores of all detected segments are shown in the bottom panel after rank sorting. In the original trace, more segments passed the LRI threshold, and their HRI scores are higher, as compared with phase-shuffled surrogates. (B) The same analysis was conducted on a 3-min current-clamp recording in vivo from an anesthetized cat, producing similar results.

Surrogates were also created by implanting artificial postsynaptic currents (PSCs) or postsynaptic potentials (PSPs) in “plain” mother traces, the timing of which was determined by a Poisson number generator (Fig. 4). As in Mokeichev et al. (2007), the amplitudes and frequencies of these PSC/Ps were altered iteratively so that the powerspectrum and current/voltage distribution of the surrogates were matched to the original traces (Fig. 4B). With regards to both the in vitro and in vivo data from Ikegaya et al. (2007), we again found that the original traces had more motif-repeats with higher HRI values (Fig. 4C).

(Ai) An 8-min voltage-clamp trace recorded from a layer 5 pyramidal cell from mouse visual cortex (blue, top) was mimicked by a Poisson process that produced a surrogate trace (red, bottom). (Aii) The same procedure was conducted on a 3-min current-clamp recording in vivo from an anesthetized cat, producing a Poisson-generated trace (red, bottom) modeled from the original (top). (B and C) Using an error-minimization algorithm, the variables used to generate the Poisson-surrogate were altered until a best fit could be made between the original and surrogate in terms of both power spectrum (B) and current/voltage distribution (C). Results displaying this goodness of fit for a single surrogate trace (red), as compared to the original (blue) are shown for both the 8-min voltage-clamp recording (Bi and Ci), and in vivo cat recording (Bii and Cii). (D) 50 Poisson surrogates were thus generated for both in vitro and in vivo recordings, and tested with the HRI detector, producing results for the in vitro mouse data (Di) and in vivo cat data (Dii). Traces in red represent the Poisson surrogate results, blue traces represent the HRI results from the original data, and the black dashed trace in Dii represents the 99% confidence interval for the Poisson surrogate results (analysis with the Jarque-Bera test of normality demonstrates that the rank ordered distributions of these scores are normally distributed for each rank order).

(A) Whole cell voltage clamp recording in vitro from a layer 5 pyramidal neuron, mouse V1 cortex. Vclamp = −70 mV. (B) Sharp electrode current clamp recording from cat visual cortex, in vivo, supragranular layer, with a large tonic hyperpolarizing current. (C) Current clamp recording from mouse cortex, in vivo and no tonic hyperpolarizing current. Note the similarities in recordings from A and B and how they both differ from C.

Interval shuffling

However, the fact that stereotypical single waveforms can be observed is not the mainissue of contention in these studies—it is whether or not these waveforms, presumablydriven by synaptic inputs from the neuronal network, can repeat in sequences of greater-than-chance precision. To address this issue, Ikegaya et al. (2004) identified the putative PSCs/PSPs using a correlationprocedure (see methods) and pulledthemout of the original recording, imposing them on a zero baseline. This procedure preserves the shape of the individual PSCs/PSPs as well as the timing of those events, creating an “extracted trace”. Surrogate traces were constructed from the extracted trace by shuffling the time intervals between the PSCs/PSPs, while preserving the temporal order of those events.

Mokeichev et al. (2007) argued that such a procedure could not be accomplished using the rat in vivo recordings because individual PSPs could not be reliably identified in most cases; we agree, and also confirm this finding with our mouse in vivo recordings. Mokeichev et al. (2007) further argued that our shuffling method may be toolenient in that trivial repeats comprised of just two PSCs/PSPs, possibly produced by the stereotypical firing pattern of a single presynaptic neuron, would be destroyed by our shuffling method; we agree with this argument as well. Their solution was to devise a shuffling technique that divided the intracellular recording into segments of approximately 400 msec. Surrogates were constructed by shuffling these segments. Thus, most of the two-event sequences are preserved in this manner.

A potential problem is that this shuffling procedure essentially shuffles the trace less thoroughly, and so the difference between surrogates and the original may not be detectable, even if deterministic repeats do exist. That is, the sensitivity of the detector program (i.e., the search program that finds repeats), may not be equipped for the task. Mokeichev et al. (2007) is aware of this caveat and tests it by injecting a 1 second long artificial repeat (i.e., absolutely deterministic) into the original recording, and then performs the 400 msec shuffling tests on this repeat-injected trace. They show that the detector does indeed distinguish the original with artificial repeat very well from the shuffled surrogates, arguing that the detector is sufficiently sensitive.

However, there is a significant problem with this sensitivity test: the LRI detector window itself is matched perfectly to the length of the artificial repeat (1 second). The basis of the detector algorithm is cross-covariance, and this function performs poorly if the detector window (set at 1 second in this program) does not match the actual length of the repeat to be detected. The original rationale for this sub-optimal detector (i.e., the LRI detection) is that it is merely a first-pass and saves much computation time. The actual values produced in the finalanalysis from HRI do not suffer from this defect since the detector window is matched to the width of the individual PSC (20 msec) or PSP (100 msec). Unfortunately, there can be many falsepositives from this 1st pass in the detector algorithm such that many candidatesnever pass the threshold for gaining HRI analysis.

We demonstrated this defect in the detector program by implanting a motif that was not matched to the LRI detector window: the implanted motif was 850 msec, in contrast to the 1 sec detector window (Fig. 6). The implanted motif consisted of a series of 5 PSPs, and this motif was summed into a 400 msec interval shuffled surrogate from a 190 second cat in vivo current clamp recording. This implanted motif was insertedevery 10 seconds, yielding 171 motif-repeat pairs. This implanted trace was then shuffled using the 400 msec interval shuffling technique, producing 50 surrogate traces. Using the LRI-HRI detector program, no difference could be found between the implanted trace and its shuffled surrogates (Fig. 6).

Figure 6

Implanting an artificial repeating motif into a shuffled recording.

(A) A 400 msec shuffled surrogate from an original cat in vivo current clamp recording is composed. A one second segment from this shuffled surrogate recording is displayed (blue) with another one second segment from 9 seconds later superimposed (red). (B) The implant: a series of PSPs is constructed from the original recording, imposed on a 0 mV baseline. (C) The implant is summed into the 1 second segments, producing an implanted trace with recurring repeats. The implants are added approximate every 10 seconds into a 190 second recording, yielding 171 repeats. (D) Fifty 400 msec shuffle surrogates are constructed from the implanted recording, and the HRI values produced from those surrogates are compared to the values produced from the unshuffled implant recording. As shown, the LRI-HRI detection algorithm does not distinguish the implanted recording from the shuffled surrogates.

Creating a better detector

In response to these results, we strived to create a detector program that could detect implanted repeats in the face of the 400 msec interval shuffle test. The goal was to create a detector that does not identify putative repeats with an arbitrary 1 second LRI window. Instead, putative repeats were detected by the onsettimes of PSPs. This new detector, PHRI (PSP-based detection, High Resolution Index), identifies the onsets of PSPs by their stereotypical risetimes, and then uses those PSP onset times as the pointers for the subsequent HRI analysis (Fig. 7). That is, every identified PSP is used as a point of alignment for a motif-repeat pair; the two selected PSPs, occurring at disparate times in the recording are aligned, and the trace that follows each is included as the motif-repeat pair to be examined. The 190 second long in vivo cat recording used in Fig. 7 contained 1351 identified PSPs, yielding 911925 motif-repeat pairs to be examined for subsequent HRI analysis—more than 100× the number of pairs identified with LRI analysis (6750 pairs). In order to reduce this substantial increase in computation time, the HRI analysis in PHRI is reduced by computing T values only for the regions identified as having PSPs (Fig. 7). In contrast, the LRI-HRI technique measures T values for every 1 msec interval of the 1 second trace (yielding 900 T valuecalculations).

Figure 7

Repeat detection with PHRI.

The onset times of putative PSPs are estimated by calculating all cross-covariance values of an average risetime waveform against the entire recording (190 seconds, in vivo cat, current clamp recording, hyperpolarized). This yields correlation values for every point in the recording, and those points with a high cross-covariance value and minimum amplitude are marked as onset time of a PSP, as shown above by the tally marks below the recording. These onset times comprise the comparisons that will be performed: n onset times yields n(n−1)/2 comparisons. One such comparison is shown above: two putative PSPs are identified with the longest blue tally and longest red tally. These PSPs are then aligned such that they yield the highest T value (using 30 msec rather than 100 msec window, see eq. 2). This alignment is preserved with respect to the comparisons made between the subsequent PSPs in each respective trace extracted from the recording. The T values are calculated for the intervals dictated by the PSP onset times in the motif trace (blue), indicated with blue arrows. T values below a set threshold are discarded from the HRI calculation, thus the black “X” indicating its non-incorporation into the HRI calculation. The minimum and maximum lengths of the motif-repeat traces that are included in the HRI calculation are 800 and 1200 msec, respectively. The minimum number of T values required for an HRI calculation are 3 (same as LRI-HRI criteria), and HRI is calculated as per eq. 3. The HRI values for all lengths between 800 and 1200 msec are calculated, and the motif-repeat length that yields the highest HRI value is saved. In the above example, the length of the motif and repeat is 853 msec, the PHRI = 5.3, and the delay between the motif and repeat is approximately 42 seconds.

As in the previous LRI-HRI technique, the criterion for a motif-repeat pair to pass HRI analysis is that it contains at least 3 regions where the T values exceed a minimum threshold. For the PHRI technique, the length of the motif-repeat is constrained to being at least 800 msec and no more than 1200 msec. The final length of the motif-repeat is defined as the length that yields the highest HRI value, and the mean length of the 10 best repeats from the cat in vivo trace in Fig. 7, using PHRI, is 933±32 msec.

The various parameters of the PHRI analysis were varied in order to enable it to distinguish the implanted trace (see Fig. 6) from shuffled surrogates. When comparing PHRI values from 50 shuffled surrogates of the implanted trace to those of the unshuffled implanted trace there appears to be a significant difference in the distribution (Fig. 8B), or at least a much great difference in the difference compared to results obtained with the LRI-HRI method (Fig. 8A).

Figure 8

The improved detector finds implanted motifs and distinguishes the original recording from its 400 msec shuffled surrogates.

(A) The original LRI-HRI detector is unable to distinguish the implanted recording from its shuffled surrogates. (B) The PHRI detector, applied to the same data set as A, appears to distinguish the unshuffled (blue) from the shuffled surrogates (red). (C) The original 190 sec cat in vivo current clamp recording and fifty 400 msec shuffle surrogates are examined with the PHRI detector. The rank ordered values from the original are shown in blue, and shuffled surrogates in red. As these values were normally distributed for each rank order, it was possible to construct confidence intervals for the distribution, and the 99% confidence interval is shown (dashed black line). The original recording results (blue line) are distinguished from the 99% confidence interval (p<0.01).

Three examples of repeats found using the PHRI detector from a 190 second long cat in vivo current clamp recording.

Each motif-repeat example is labeled with its respective PHRI and its length. The PHRI values are a subset of those that make up the full set of PHRI values for this recording that are displayed in Fig. 8c.

Revisiting recording conditions: an experiment

Having convincedourselves that some in vivo and in vitro recordings show evidence of significantly repeating patterns, we then addressed a previously discussed hypothesis: repeats of synaptic inputs are better detected during hyperpolarized membrane potentials. To this end, we recorded a neuron from mouse somatosensory cortex, in vivo, in current clamp at approximately −60 mV resting membrane potential, and then applied a DC hyperpolarizing current, bringing the membrane potential to approximately −90 mV. This particular recording allowed the identification of some PSPs at −60 mV, but PSPs appeared to be more easily detectable at −90 mV (Fig. 10A,B). Both HRI and PHRI analysis yielded significantly higher values for the −90 mV section of the recording versus the −60 mV section (p<0.01 Kolmogorov-Smirnoff tests for each analysis, 100 seconds of recording in −60 mV and −90 mV). Furthermore, when fifty 400 msec shuffled surrogates were created for each, the −90 mV section of the recording exceeded the distribution by a significantly greater margin, exceeding 99.9% confidence intervals (Fig. 10C).

Figure 10

Effect of membrane potential hyperpolarization on PSP detection.

(A) A sample of an in vivo current clamp recording is shown at an approximate resting membrane potential of −55 mV (top) versus a sample recorded from the same neuron minutes later at −95 mV (bottom). The hyperpolarized membrane potential was induced by a tonic DC injection. Underlined segments of these recordings are expanded in (B), showing the increased ability to detect smaller PSPs during hyperpolarized membrane potentials. (C) PHRI values recorded during resting membrane potential versus artificially induced hyperpolarized membrane potentials. (top) PHRI values are calculated from 90 seconds of resting membrane potential recording (mean −55 mV) (blue trace) and compared to 50 shuffle surrogates (red traces). Black dashed line represents the 99.9% confidence interval for the 50 shuffle surrogates. (bottom) The same results are shown, but with regards to 90 seconds of recording at hyperpolarized membrane potential (mean −90 mV), from the same neuron. The PHRI values obtained from the hyperpolarized section of recording (bottom) were significantly greater than the PHRI values obtained from the resting membrane potential recording (top) (p<0.001, Kolmogorov-Smirnoff test).

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Discussion

Based on our new analysis and data, we believe that the basic conclusions from Ikegaya et al. (2004) with regards to the analysis of the intracellular recordings remainvalid. The data presented in that paper pass the surrogate tests presented in Mokeichev et al. (2007), although with the caveat that the repeat detector used in both of those papers was problematic. We further conclude that the phase randomization surrogates do not advance this study for generating surrogates, given the fact that they destroy the PSC/PSP structure of intracellular recordings.

We also conclude that the Poisson surrogates do not offerinsight into the rootquestion of this study. Unlike the phase randomization surrogates, they can at least imitate PSC/PSPs and thus retain these inherent, short repeats. In generating these surrogates, we reached the same conclusion as in Ikegaya et al. (2004), i.e., the surrogates contain significantly fewer repeats than the original. However, the argument against the surrogate data in Ikegaya et al. (2004) can also be used against these surrogates: the possibly trivial two consecutive PSC/PSP sequences are not conserved. Therefore, we conclude that the Poisson surrogates in this study do not resolve the root controversy.

It may be worthnoting that it is much easier to generate Poisson surrogates that are very well-matched to original traces from in vitro, voltage-clamp recordings, as compared to in vivo current clamp recordings, as seen in the power spectrum and voltage distribution (Figs. 4B and 4C). This may not be surprising as the current clamp recordings should contain more intrinsic voltage-gated responses that require a more complicated model than that offered in this study. Indeed, the match in power spectrum and voltage distributions from the Poisson surrogates generated in Mokeichev et al. (2007) appear to be ill-matched to the original recordings (Fig. S2, Mokeichev et al., 2007). Furthermore, power spectrum and amplitude distributions are only two means of matching surrogates to original, and may exclude other important qualities of the original data. These problems in matching Poisson surrogate data to original data further undermine the results of this technique.

However, the 400 msec interval shuffling technique offered by Mokeichev et al. (2007) is a significant advance, and we focus on this particular surrogate generating technique for the remainder of the discussion. The interval shuffling technique inspired a re-examination of the original study and detection technique, and we discovered some flaws in the latter. In particular, the stated average repeat length of approximately 1 second reported in Ikegaya et al. (2004) should not be considered the true average length of repeats found intracellularly, but rather, an artificeresulting from the repeat detector program itself. That is, the initial LRI search in the detector program looks for repeats that are 1 second in duration—the repeat length itself is predetermined by the initial search window, which, as stated in Ikegaya et al. (2004), was chosen arbitrarily. The actual lengths of deterministic repeats in these networks are not indicated by these methods. This is a shortcoming of the detector program we originally used.

Another shortcoming, as revealed to us by results from Mokeichev et al. (2007), is the fallibility of using cross-covariance as a measure for similarity. This flaw is demonstrated by the detector's inability to distinguish a trace with implanted repeats from shuffled surrogates (Fig. 6). This finding suggests that if the initial detector window (1 second) is not matched to length of the repeat (in this case, 850 msec), then a false-negative result can be produced. This shortcoming is not so much a problem in the HRI detection part of the algorithm as the detector window is matched to the length of the synaptic events (between 20 msec and 100 msec). However, as the HRI algorithm scans only those sections of the recording indicated by the LRI search, then the entire LRI-HRI detector is compromised by the failing in the LRI.

In order to address these concerns, we devised a new detector, PHRI (Fig. 7). This detector differed from the previous in two ways: (1) putative repeats, to be carriedover to HRI analysis, are selected based on the onset times of PSPs; (2) the algorithm that scans the putative repeats, creating T values, does not measure every 100 msec interval, but rather measures each interval as indicated by the onset times of the PSPs (Fig. 7). As for (1), this prevents the mistakesinvoked by using an a priori 1 second detector window, and (2) reducesgreatly the number of T calculations, yielding a faster analysis. This new detector distinguishes the implanted trace from shuffled surrogates (Fig. 8). In addition, the original cat in vivo recording is distinguished from shuffled surrogates in the rankings of repeat indices found in those recordings (p<0.01).

However, the question remained, why are some intracellular recordings, such as in vitro voltage clamp recordings, or the cat in vivo current clamp recording presented here, so different from the other in vivo current clamp recordings? The original idea of our method was to record the activity of many neurons in a synaptic network by recording the intracellular activity of just one neuron embeddedwithin that network. This idea is not tested if the synaptic events are not resolved. The blurring of synaptic events could occur during current clamp recordings as the intrinsic voltage responses of the neuron are allowed to influence the recording. In addition, sharpelectrode recordings may not revealsmaller synaptic events, in comparison to whole-cell recordings, perhaps allowing even greater reduction of synaptic events relative to the intrinsic voltage fluctuations. It is also conceivable that this technique is inappropriate for in vivo recordings where the number of synaptic inputs is so great that resolving them individually is not feasible with a recording at the soma alone.

These speculations do not address the current clamp sharp electrode recording from cat cortex, in vivo, where significant repeats could be found using all shuffle surrogates tested. One feature of this recording that distinguishes it from the rat in vivo recordings so far reported is the large tonic hyperpolarizing current that was applied to the neuron. This current was applied to prevent action potentials from occurring, in accordance with the protocols from Lampl et al. (1999) [26]. It is conceivable that such a large hyperpolarizing current may prevent many voltage-gated channels from operating, especially as many of those channels are activated at more depolarizedlevels. In addition, it's possible that the neuron is held either at or hyperpolarized to the GABA-A reversal potential. Thus, all synaptic events are either stronglydepolarizing or negligible, allowing a flat baseline upon which these currents may be resolved. We tested these ideas by recording a neuron from mouse somatosensory cortex in vivo in current clamp where half of the recording was at a membrane potential of about −60 mV, and the latter half at −90 mV. We demonstrate that the repeats found at −90 mV have a significantly greater distribution of repeat indices than those at −60 mV (p<0.001), and we show that this recording also has a greater distribution than its shuffled surrogates (p<0.001) (Fig. 10).

Cat in vivo recordings: neurons in supragranular cortex in area V1 were recorded intracellularly with sharp electrodes filled with 2 M potassiumacetate. The adult cats were paralyzed and barbiturate-anesthetized, and no stimulation was given during the recordings (spontaneous activity only). For the recording analyzed in this study, a tonic hyperpolarizing current was applied to prevent spontaneous action potentials, and the recording was stable for 10 minutes. Further details of the in vivo recordings can be found in Lampl et al. (1999) [26] and Chung and Ferster (1998) [27].

Analysis

Finding repeats of intracellular activity: LRI-HRI method

The technique discussed here uses intracellular recordings from single neurons as a means to “listen” to potentially all of the activity of all neurons that formsynapses with that recorded neuron. As a single pyramidal neuron may receive 1000 s of synapses from other neurons, most of them locally, then this technique has the potential to yield information about a large fraction of a cortical column (Fig. 1). This procedure for finding repeats of intracellular activity has been described in Ikegaya et al. (2004) [7] as well as Mokeichev et al. (2007) [24]. There are two stages in the search for repeats: (1) a low resolution search, producing a low resolution index (LRI) and (2) a high resolution search, producing a high resolution index (HRI). Both methods are forms of template matching: two segments are isolated from a long recording and the similarity between those segments is quantified.

Low Resolution Index (LRI)

The LRI compares 1 second segments of the recorded waveform, using a nested loop of template matching (Fig. 2). The cross-covariance function is at the heart of this analysis, and this function quantifies the temporal similarities of the recorded waveforms.(1)

Here, x and y are amplitudes from the respective motif and its potential repeat, and 2T+1 are the number of samples in each motif at 1 point per msec. The length of x and y are 1 second (1000 points at 1 point per millisecond), and τ represents the lag time between x and y. The motifs and repeats are defined by these lengths and the incrementaljump from one potential repeat to another is 250 msec (in Fig. 2 this would represent the incremental movements of the colored brackets). As jumps of 250 ms are unlikely to find the regions of precise overlap, the program realigns the traces according to the difference between the peak value of the covariance function and the zeroeth lag of this function (i.e., the value at τ = 0) and then recomputes the function, provided that the peak value is initially within 250 ms of the zeroeth lag. The value at the zeroeth lag (h(0)) is then recorded. The highest values for each 1 second interval and those passing a set threshold were collected for each recording and formed our low resolution similarity index (LRI). The threshold was set according to a level that yielded a reasonable number of putative motif-repeats that could be analyzed with subsequent HRI analysis. “Reasonable” is defined here as taking less than a fewdays of computation time with HRI analysis, and per recording this would mean on the order of 10000 putative repeats. In most recordings the threshold was set to approximately 0.45. In this sense, the thresholds here not considered definitive.

The 1 second length of the motif and repeats is also arbitrary, and, as discussed later, problematic. This initial identification is, however, somewhatjustified in reducing what would otherwise be an overlyburdensomecomputational task. That is, the LRI is used to identify putative repeats, remember the locations of those putative repeats, and then analyze more carefully those segments in subsequent analyses. Segments that do not pass a minimum threshold are passed over and not analyzed further, saving some time in the subsequent intensive analysis.

Hig Resolution Index (HRI)

(2)(3)

Those threshold-passing motif-repeats identified with the LRI are saved later for calculation of HRI. For HRI, the two 1 second segments are compared in greater detail as cross-covariance functions are computed for every 20 msec interval between the two 1 second segments (Fig. 2). This 20 msec interval is determined by the average width of a PSC. When recording PSPs in current clamp, the charging of the membrane results in longer synaptic signals, and in those cases 100 msec intervals are used. In both cases, it is important that the width of the cross-covariance window is matched to the mean estimated duration of an individual synaptic event. The HRI is computed from the number of threshold-passing 20 msec intervals, the similarity measured in each of those 20 msec intervals (T values, Eq. 2), as well as a general similarity index for the entire duration of the putative repeat (Eq. 3).

Finding repeats of intracellular activity: PHRI method

The newer method, PHRI, differs from the LRI-HRI method mostly in terms of how putative repeats are detected: rather than using cross-covariance of 1 second samples from the recording, the PHRI identifies potential repeats by the onset times of identified PSPs (or PSCs) (Fig. 7). The PSPs are identified by their risetimes in a method nearly identical to that from Ikegaya et al. (2004) with regards to the extraction of PSPs in that paper: PSPs were detected by computing a covariance function of a mean PSP rise time waveform (4–6 msec in duration) against the entire spontaneous recording: this produced a waveform whosepeaksmarked the onset of PSPs, and peaks passing a set threshold (typically, 0.9) were taken as the start times of PSPs. In some cases, an amplitude threshold was used in conjunction with the covariance function threshold. Thresholds were adjusted so that the fewest false positives and false negative results appeared, as can be judged in viewingFig. 7. Importantly, the number of identified PSPs found in surrogate traces versus original traces was unchanged by the creation of 400 msec shuffled surrogate traces.

The identified onset times of PSPs were then used as the points of alignment for comparing two different stretches of a recording, called here a putative motif-repeat (Fig. 7). T values (Eq. 2) are then calculated at these aligned motif-repeats, but in contrast to LRI-HRI analysis, the T values are only calculated at the onset times of PSPs found in the motif of the motif-repeat. These T values are then used just as before in the calculation of HRI (Eq. 3). With this PHRI technique, the length of the motif-repeat is determined by length that yields the highest HRI value, and it is constrained by having a minimum of 800 msec and a maximum of 1200 msec. This constraint is enacted with respect to the shuffle surrogate technique described below: if motif-repeats are allowed that are the same length of the shuffle lengths (400 msec), then the shuffling is likely to keep many of the motif-repeats intact (it would be analogous to using the LRI-HRI technique and shuffling with 1000 msec segments). As in the LRI-HRI technique, a minimum of three T values that pass threshold are required.

Surrogate traces

The production of surrogate traces was performed using three methods described in Mokeichev et al. (2007), namely, phase randomization, Poisson simulation, and interval shuffling. The phase randomization technique performs a fast Fourier transform (FFT) of the original trace, decomposing it into its frequency components. There is a particular phase and amplitude associate with each component, and in this shuffle technique the original phases are replaced with randomly chosen phases. After a reverse FFT, a surrogate trace is produced where the temporal relationships between its various frequency components have been randomized with respect to the original, while the frequency power spectrum remains the same.

The Poisson simulation creates surrogate traces by stimulating a single model neuron with synaptic inputs. The relative strengths and frequencies of these inputs are manipulated so that the simulated recording in the model neuron produces a surrogate trace that is similar with respect to the original with regards to power spectrum and voltage (or current) distribution.

The interval shuffling protocolarguably randomizes the original trace the least thoroughly, and so is the most rigorous shuffling protocol. In this, the original trace is “cut” into segments of approximately 400 msec long. These segments are then randomly reattached to each other, with certainconstraints so that no artificially abruptchanges in voltage are introduced. The “cut points” are determined by two different voltage levels that are chosen according to the lower third and upper third of the total voltage amplitude distribution. This is a shuffling in the time domain, and produces surrogates with the same power spectrum and voltage distribution[24].

The surrogate trace generation techniques were implemented using Igor software (Wavemetrics). The search for repeats in these and original traces were conducted using Matlab (Mathworks) software on a 288-unitclustercomputer.

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Ikegaya et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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